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Free, publiclyaccessible full text available June 16, 2023

In the Proceedings on the 11th International Conference on Probabilistic Graphical Models (PGM), published as part of the PMLR series.Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available January 1, 2023

We propose that approximate Bayesian algorithms should optimize a new criterion, directly derived from the loss, to calculate their approximate posterior which we refer to as pseudoposterior. Unlike standard variational inference which optimizes a lower bound on the log marginal likelihood, the new algorithms can be analyzed to provide loss guarantees on the predictions with the pseudoposterior. Our criterion can be used to derive new sparse Gaussian process algorithms that have error guarantees applicable to various likelihoods.

The paper introduces a new algorithm for planning in partially observable Markov decision processes (POMDP) based on the idea of aggregate simulation. The algorithm uses product distributions to approximate the belief state and shows how to build a representation graph of an approximate actionvalue function over belief space. The graph captures the result of simulating the model in aggregate under independence assumptions, giving a symbolic representation of the value function. The algorithm supports large observation spaces using sampling networks, a representation of the process of sampling values of observations, which is integrated into the graph representation. Following previous work in MDPs this approach enables action selection in POMDPs through gradient optimization over the graph representation. This approach complements recent algorithms for POMDPs which are based on particle representations of belief states and an explicit search for action selection. Our approach enables scaling to large factored action spaces in addition to large state spaces and observation spaces. An experimental evaluation demonstrates that the algorithm provides excellent performance relative to state of the art in large POMDP problems.

This paper investigates online stochastic planning for problems with large factored state and action spaces. One promising approach in recent work estimates the quality of applicable actions in the current state through aggregate simulation from the states they reach. This leads to significant speedup, compared to search over concrete states and actions, and suffices to guide decision making in cases where the performance of a random policy is informative of the quality of a state. The paper makes two significant improvements to this approach. The first, taking inspiration from lifted belief propagation, exploits the structure of the problem to derive a more compact computation graph for aggregate simulation. The second improvement replaces the random policy embedded in the computation graph with symbolic variables that are optimized simultaneously with the search for high quality actions. This expands the scope of the approach to problems that require deep search and where information is lost quickly with random steps. An empirical evaluation shows that these ideas significantly improve performance, leading to state of the art performance on hard planning problems.

It is well known that the problems of stochastic planning and probabilistic inference are closely related. This paper makes two contributions in this context. The first is to provide an analysis of the recently developed SOGBOFA heuristic planning algorithm that was shown to be effective for problems with large factored state and action spaces. It is shown that SOGBOFA can be seen as a specialized inference algorithm that computes its solutions through a combination of a symbolic variant of belief propagation and gradient ascent. The second contribution is a new solver for Marginal MAP (MMAP) inference. We introduce a new reduction from MMAP to maximum expected utility problems which are suitable for the symbolic computation in SOGBOFA. This yields a novel algebraic gradientbased solver (AGS) for MMAP. An experimental evaluation illustrates the potential of AGS in solving difficult MMAP problems.